Behaving like atomically-precise two-dimensional quantum wells with non-negligible dielectric contrast, the layered HOIPs have strong electronic interactions leading to tightly bound excitons with binding energies on the order of 500 meV. These strong interactions suggest the possibility of larger excitonic complexes like trions and biexcitons, which are hard to study numerically due to the complexity of the layered HOIPs. Here, we propose and parameterize a model Hamiltonian for excitonic complexes in layered HOIPs and we study the correlated eigenfunctions of trions and biexcitons using a combination of diffusion Monte Carlo and very large variational calculations with explicitly correlated Gaussian basis functions. Binding energies and spatial structures of these complexes are presented as a function of the layer thickness. The trion and biexciton of the thinnest layered HOIP have binding energies of 35 meV and 44 meV, respectively, whereas a single exfoliated layer is predicted to have trions and biexcitons with equal binding enegies of 48 meV. We compare our findings to available experimental data and to that of other quasi-two-dimensional materials.
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